## Knots and Random Walks in Vibrated Granular Chains,

### E. Ben-Naim, Z.A. Daya, P. Vorobieff, and R.E. Ecke

We study experimentally statistical properties of the opening times of
knots in vertically vibrated granular chains. Our measurements are in
good qualitative and quantitative agreement with a theoretical model
involving three random walks interacting via hard core exclusion in
one spatial dimension. In particular, the knot survival probability
follows a universal scaling function which is independent of the chain
length, with a corresponding diffusive characteristic time scale. Both
the large-exit-time and the small-exit-time tails of the distribution
are suppressed exponentially, and the corresponding decay coefficients
are in excellent agreement with the theoretical values.

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